Question

describe the relationship between the two graphs.
note that f = 0 where f has a minimum. also note that f is negative when f is decreasing and f is positive when f is increasing.
note that f = 0 where f has a minimum. also note that f is decreasing when f is negative and f is increasing when f is positive.
note that f = 0 where f has a minimum. also note that f is decreasing when f is negative and f is increasing when f is positive.
note that f = 0 where f has a maximum. also note that f is positive when f is decreasing and f is negative when f is increasing.
note that f = 0 where f has a minimum. also note that f is positive when f is decreasing and f is negative when f is increasing.
note that f = 0 where f has a maximum. also note that f is negative when f is decreasing and f is positive when f is increasing.

Explanation:

The derivative $f'$ of a function $f$ is zero at the critical - points (maximum or minimum). When $f$ is increasing, $f'>0$ and when $f$ is decreasing, $f'<0$. At a maximum of $f$, the slope of the tangent line (i.e., $f'$) is zero, and $f'$ changes sign from positive to negative. At a minimum of $f$, the slope of the tangent line (i.e., $f'$) is zero, and $f'$ changes sign from negative to positive.

Answer:

Note that $f' = 0$ where $f$ has a maximum. Also note that $f'$ is negative when $f$ is decreasing and $f'$ is positive when $f$ is increasing.